3 papers
math.AP2022
Weak solutions of 3D compressible Navier-Stokes equations in critical case
Pavel I. Plotnikov
New estimates of the potentials of solutions to the compressible Navier-Stokes equations are derived. The result obtained are applied to boundary value problems for the compressibl…
math.AP2020
A Proof of Hélein's Conjecture on Boundedness of Conformal Factors when n=3
P. I. Plotnikov, J. F. Toland
For smooth mappings of the unit disc into the oriented Grassmannian manifold , Hélein (2002) conjectured the global existence of Coulomb frames with bounded confor…
math.DS2015
Kolmogorov's Theorem for Low-Dimensional Invariant Tori of Hamiltonian Systems
Pavel Plotnikov, Ivan Kuznetsov
In this paper the problem of persistence of invariant tori under small perturbations of integrable Hamiltonian systems is considered. The existence of one-to-one correspondence bet…